Multi-core Real-Time Scheduling for Generalized Parallel Task Models Abusayeed Saifullah, Kunal Agrawal, Chenyang Lu, Christopher Gill

 Multi-core processors provide an opportunity to schedule computation-intensive tasks in real-time  Most of the tasks exhibit intra-task parallelism  Real-time systems need to be developed to exploit intra-task parallelism 2 Real-Time Systems on Multi-core  Traditional multiprocessor scheduling  Focuses on inter-task parallelism  Mostly restricted to sequential task models  Computation-intensive complex real-time tasks are growing  Video surveillance  Radar tracking  Hybrid real-time structural testing

3 Parallel Task Model  Lakshmanan et al. (RTSS ’10) have addressed a restricted synchronous model where Each horizontal bar indicates a thread of execution (sequence of instructions) Parallel threads form a segment Threads of each segment synchronize at the end of the segment  A task is an alternate sequence of parallel and sequential segments  The total number of threads in each segment ≤ number of cores  All parallel segments have an equal number of threads  Synchronous task model Segment 1 Seg 2 Seg 3 Segment 4 Segment 5 Threads of Segment 1 synchronize here

Our Contributions 4  We address a general synchronous parallel task model  Different segments may have different numbers of threads  Each segment can have an arbitrary number of threads  Example: such tasks are generated by  Parallel for loops in OpenMP, CilkPlus  Barrier primitives in thread libraries  This model is more portable  The same program can execute on machines with different numbers of cores

A Task Example start end 5 void parallel_task(float *a,float *b,float *c,float * d) { 7 int n=7; int i=0; parallel_for(; i< n; i++) c[i] = a[i] + b[i]; n=4; i=0; parallel_for(; i< n; i++) d[i] = a[i] - b[i]; }

Our Contributions (contd..) 6  We propose a task decomposition for general synchronous parallel task model  Decomposes each parallel task into a set of sequential subtasks  Subtasks are scheduled like traditional tasks  Why decomposition?  We can exploit the rich literature of multiprocessor scheduling  The proposed decomposition ensures that if the decomposed tasks are schedulable, the original task set is also schedulable

Our Contributions (contd..)  We analyze schedulability in terms of processor speed augmentation bound  Speed augmentation bound ν for an Algorithm A: if an optimal algorithm can schedule a synchronous parallel task set on unit- speed processor cores, then A can schedule the decomposed tasks on ν-speed processor cores.  We prove that the proposed decomposition requires a speed augmentation of at most  4 for Global Earliest Deadline First (G-EDF) scheduling  5 for Partitioned Deadline Monotonic (P-DM) scheduling 7

Overview of a Task Decomposition 8  Each thread of the task becomes an individual task with  An intermediate subdeadline  A release offset to retain precedence relations in the original task  Deadlines are assigned by distributing slack among segments  Deadline of a thread= execution requirement+ assigned slack

 How much slack a segment demands depends on  Available slack of the task  Execution requirement of the segment  Execution requirement of a segment is the product of  Total number of parallel threads in the segment and  Execution requirement of each thread in the segment  Larger execution requirement implies more demand for slack  In the figure, Segment 1 requires more slack than Segment 2 Slack Distribution 9

Slack Distribution (contd..) 10  We use the following principle to distribute slack  All segments that receive slack will achieve an equal density  Reasons to equalize the density among segments  Fairness: deadline of each segment becomes proportional to its execution requirement  We can bound the density of the decomposed tasks  We can exploit existing density-based analyses for multiprocessor

Slack Distribution (contd..) 11 …  Slack of each segment is determined by solving the equalities  Sum of subdeadlines=task deadline (total assigned slack = task slack)  Density of Segment 1= density of Segment 2 = so on  All threads in a segment have the same deadline and offset  Deadline= execution requirement of the thread + segment slack  Release offset=sum of deadlines of preceding segment

An Example of Task Decomposition 12 Segment 1: deadline=20 density= (5*4)/20=1 Segment 2: deadline=4 density= (2*2)/4=1 Segment 3: deadline=9 density= (3*3)/9=1 Segment 4: deadline=16 density= (4*4)/16=1 Segment 5: deadline=3 density= (1*3)/3=1 All segments have an equal density!

Global EDF (G-EDF) Schedulability  A sufficient condition for G-EDF scheduling on m unit- speed cores [Baruah RTSS ’07]  A necessary condition for any task set for any scheduler total density max density If the original task set is schedulable anyway on m unit-speed cores, the decomposed tasks are schedulable under G-EDF on 4-speed cores Using the density bounds for decomposed tasks 13

Partitioned DM (P-DM) Schedulability  A sufficient condition for FBB-FFD scheduling on m unit-speed cores FBB-FFD (Fisher Baruah Baker – First-Fit Decreasing) is a well-known P-DM scheduler [ECRTS ’06]  A necessary condition for any scheduler max cumulative exe. req. of tasks divided by time length If the original task set is schedulable anyway on m unit-speed cores, the decomposed tasks are FBB-FFD schedulable on 5-speed cores Using load and density bounds for decomposed tasks 14

Conclusion  Multi-core processors provide opportunities to schedule computation-intensive tasks in real-time  Real-time systems need to exploit intra-task parallelism  We have addressed real-time scheduling for generalized synchronous parallel task model  Different segments may have different number of threads  Each segment can have an arbitrary number of threads  We have proposed a task decomposition that achieves  A processor-speed augmentation bound of 4 for Global EDF  A processor-speed augmentation bound of 5 for Partitioned DM 15